Question: Umaima is 15 years older than Jessica. Umaima and Jessica first met 3 years ago. Twenty years ago, Umaima was 4 times older than Jessica. How old is Umaima now?
Explanation: We can use the given information to write down two equations that describe the ages of Umaima and Jessica. Let Umaima's current age be $u$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $u = j + 15$ Twenty years ago, Umaima was $u - 20$ years old, and Jessica was $j - 20$ years old. The information in the second sentence can be expressed in the following equation: $u - 20 = 4(j - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = u - 15$ . Substituting this into our second equation, we get the equation: $u - 20 = 4($ $(u - 15)$ $ -$ $ 20)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $u - 20 = 4u - 140$ Solving for $u$ , we get: $3 u = 120$ $u = 40$.